According to the model selection the best model structure is: y ~ x1 + x2 + x4 + error. Now we’re going to test the model further.
Construct X matrix
Split into train-test
Fit model, generate predictions, compute error (SSE, MSE) and adjusted R^2.
## MSE is: 0.01069316
## Adjusted R^2 is: 0.9999891
Numerical analysis
## Residual analysis:
## Min 25% Median 75% Max
## -0.305319926 -0.061646247 0.008535535 0.077296305 0.291481680
##
## Residual mean: 0.007
##
## Residual mode: 0.013
## [,1] [,2] [,3]
## [1,] 5.1e-05 1.0e-05 -2e-06
## [2,] 1.0e-05 4.5e-05 -5e-06
## [3,] -2.0e-06 -5.0e-06 1e-06
Because we have 3 parameters, we’ll need to plot all their combinations resulting in 3 plots.
First we create grid of possible parameter values for which we estimate the uncertainty.
Now we can calculate the pdf
Now we’ll generate predictions on training data and 95% confidence intervals
Plot the predictions + CI
Validate the model on new train-test split - 70:30
Construct X matrices (train and test)
Re-use the fitting function from model selection
Fit model on training data and predict testing data
## MSE on training data = 0.01094003
## MSE on testing data = 0.008348671